Design and Implementation of a Data-Oriented Nonlinear PIDController

PID control schemes have been widely used in most industrial control systems. However, it is difficult to determine a suitable set of PID gains, because most industrial systems have nonlinearity. On the other hands, Cerebellar Model Articulation Controller (CMAC) classified as neural networks has been proposed, and design scheme of an intelligent PID controller by using the CMAC-PID tuner has been proposed. However, the CMAC-PID tuner has two problems. One is that the CMAC must be trained in an online manner to get their optimum weights. Another is that the CMAC requires lots of memories and high computational cost for some microcontrollers. In order to train CMAC in an offline manner, CMACFRIT scheme which is a combination of CMAC and Fictitious Reference Iterative Tuning (FRIT) scheme has been proposed in a previous research. FRIT is a scheme to determine control parameters by using a set of experimental data. According to the CMAC-FRIT scheme, CMAC-PID tuner can be trained in an offline manner by using a set of operating data. In this paper, to address the problem of required memory and computational cost, a method that expresses CMAC-PID tuner as a simple nonlinear function by using Group Method of Data Handling (GMDH) is proposed. According to the proposed method, CMAC-PID tuner (which is trained in advance by using a set of operating data) is replaced by a network of N-Adalines (units expressed by a simple nonlinear function). Thus, the proposed algorithmcan be easily added to a microcontroller even if it is a commodity type. The effectiveness of the proposed method is validated by a simulation example. Moreover, to show the usefulness of the proposed method, the algorithm is added to a commodity type microcontroller, and the controller is applied to a magnetic levitation device.